Life at the Landau pole

Abstract

If a quantum field theory has a Landau pole, the theory is usually called 'sick' and dismissed as a candidate for an interacting UV-complete theory. In a recent study on the interacting 4d O(N) model at large N, it was shown that at the Landau pole, observables remain well-defined and finite. In this work, I study both relevant and irrelevant deformations of the said model at the Landau pole, finding that physical observables remain unaffected. Apparently, the Landau pole in this theory is benign. As a phenomenological application, I compare the O(N) model to QCD, by identifying ${\Lambda }_{\overline{\mathrm{MS}}}$ with the Landau pole in the O(N) model.

24 pages, 6 figures; v2: typos fixed, slightly expanded discussion; v3: expanded discussion, more typos fixed, matches version accepted for publication

References in corpus (6)

• The QCD transition temperature: results with physical masses in the continuum limit II.
• Resonantly-paired fermionic superfluids
• $\mathcal{P}\mathcal{T}$-symmetric $-g{\phi }^4$ theory
• Simple non-perturbative resummation schemes beyond mean-field: case study for scalar ${\varphi }^4$ theory in 1+1 dimensions
• Three dimensional Yukawa models and CFTs at strong and weak couplings
• Following Gluonic World Lines to Find the QCD Coupling in the Infrared

Cited by in corpus (2)

• Exact quantization conditions and full transseries structures for $\mathcal{P}\mathcal{T}$ symmetric anharmonic oscillators
• Rescuing 331 bileptons from the Landau pole